An abstract functional framework is developed for the dual Petrov-Galerkin formulation of the initial boundary value problems with a third-order spatial derivative. This framework is then applied to study the wellposedness and decay properties of Airy equation and KdV equation in a finite interval.

1Max-Born-Institute for Nonlinear Optics and Ultrafast Spectroscopy, 2A Max-Born-Str., D-12489 Berlin, Germany, 2Special Technologies, Ltd., 1/3 Zeljonaja gorka Str., 630060 Novosibirsk, Russia, 3Research Laboratory of Quantum Optics Technology, Novosibirsk State University, 2 Pirogova Str., 630090 Novosibirsk, Russia, 4Department of Applied Physics, Royal Institute of Technology, 10691 Stockho...

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov,* S. Kotochigova, J. Ye, and D. S. Jin JILA, National Institute of Standards and Technology and University of Colorado, and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA Department of Physics, Temple University, Philadelphia, Pennsylvania 19122-6082, USA (Received 10 September 2012; published...

A level set method combining features of front tracking methods and fixed domain methods is presented to model microstructure evolution in the solidification of multi-component multiphase alloy systems. Phase boundaries are explicitly tracked by solving the multi-phase level set equations. Diffused interfaces are constructed by extending a small width in both directions from these explicitly tr...

We present a new two-parameter family of solutions of Einstein gravity with negative cosmological constant in 2+1 dimensions. These solutions are obtained by squashing the anti-deSitter geometry along one direction and posses four Killing vectors. Global properties as well as the four dimensional generalization are discussed, followed by the investigation of the geodesic motion. A simple global...

Obtaining genomic data from large numbers of species has now become a feasible reality. In comparative genomics, these data serve to understand the way in which DNA sequences are affected by different evolutionary processes (e.g. selection, genetic drift and mutation bias). One important question that can be addressed is what fraction of genes and nucleotide sites have been subject to positive ...

In this paper we consider the action of symplectic feedback transformations on 1-D control Hamiltonian systems. We study differential invariants of the pseudogroup of feedback symplectic transformations, which we call Petrov invariants, and show that the algebra of invariants possesses a natural Poisson structure and central derivations. This structure allows us to classify regular 1-D control ...

This article introduces results about probabilistic parsing enhanced with a word clustering approach based on a French syntactic lexicon, the Lefff (Sagot, 2010). We show that by applying this clustering method on verbs and adjectives of the French Treebank (Abeillé et al., 2003), we obtain accurate performances on French with a parser based on a Probabilistic ContextFree Grammar (Petrov et al....

This paper considers large deviation results for sums of independent random variables, generalizing the result of Petrov (1968) by using a weaker and more natural condition on bounds of the cumulant generating functions of the sequence of random variables. MSC 60F10, 60G50, 62E20.

We present new exact solutions of the Einstein-Yang-Mills system. The solutions are described by a null Yang-Mills field in a Kundt spacetime. They generalize a previously known solution for a metric of pp wave type. The solutions are formally of Petrov type III.